In a statement he said he could not " fully rationalise" why it was such a struggle for him - and many others - but had come to understand " the only way to be truly happy on a personal level is to acknowledge in public as well as in private, who I am".

"I so admire the many people, young and old, who are doing this every day, uncertain of the reaction. I have been very fortunate and couldn't have had more love and support from my family and friends," the father-of-three wrote on his website.

"However, making this public is something I have had to do myself. I don't know what the wider reaction will be, but I know it's the right thing for me to do.

"Other than the intensely personal and positive difference it makes to me, and the way I can live my life, my hope is that my coming out doesn't change anything else about how I go about my work or how people treat me.

"Gender and sexuality should make no difference whether you are a cabinet minister or in any other walk of life and I hope that I can, in my own way, reinforce that message."

His son Oliver wrote on Twitter: "I admire my dad as much today as I did yesterday. Brave decision to go public and the right one."

The leader of the Scottish Conservative Party, Ruth Davidson - who is also gay - said her colleague had her " wholehearted support, as well as the support of the wider Scottish Conservative family".

"I know that David didn't make today's statement lightly, but approached it in his typically thoughtful and positive manner," she wrote on Twitter.

A senior Downing Street source said David Cameron had been informed in the past few days of Mr Mundell's decision to issue a statement.

Asked if the Prime Minister offered his warm support to the Scotland Secretary, the source said: "Of course, absolutely."

He added: "I'm not going to get into their private conversation, and it's obviously a very personal statement, but the PM is very pleased and delighted that he is in a position to take this step, and it's very encouraging to see."

Challenged over why it had taken so long for the Conservatives to have their first openly gay Cabinet minister, the source said: "To be honest, I think the PM, in terms of the Cabinet, appoints people on merit. I don't think he really thinks about issues like that.

"There have been other ministers in the Prime Minister's Government who have been gay. People tend to be appointed on merit and their ability to do the job."

Scotland's First Minister Nicola Sturgeon tweeted her support to Mr Mundell, saying: "Good on you, David. Well done and best wishes."

Mr Mundell's announcement brings the number of openly-gay and bisexual MPs to 34 - the highest proportion of any Parliament in the world, according to a study by US academics - and means there are now more "out" Tories (14) than Labour (13).

Colin Macfarlane, director Stonewall Scotland said: " We're so happy David Mundell feels able to speak openly about his sexual orientation. Having high profile people across all areas of society, from politics to sport, is crucial to creating inclusive environments and helping ensure the fair treatment of lesbian, gay, bi and trans people at work, at home and in their communities.

"Role models like David Mundell also inspire young lesbian, gay, bi and trans people by letting them know they are not alone and that they too can feel proud of their identity."